More on Lebesgue Integral and Measure
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Our objective in this chapter is to add a few more topics to Lebesgue’s theory of measure and integration introduced in Chap. 10. We begin by revisiting the connection to Riemann’s theory and give a short discussion of improper Riemann integrals. Next, we look at integrals depending on a parameter and give sufficient conditions under which the order of limits and integrals may be interchanged as well as conditions that guarantee the possibility of differentiating under the integral sign.
KeywordsLebesgue Integral Improper Riemann Integral Absolute Continuity Shadow Points Lebesgue Theory
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